[Studies in Computational Intelligence 481] Artur Babiarz, Robert Bieda, Karol Jędrasiak, Aleksander Nawrat (auth.), Aleksander Nawrat, Zygmunt Kuś (eds.) - Vision Based Systemsfor UAV Applications (2013, Sprin

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262 H. Josiński et al. Table 6. Two class problems, experiment 2 TP TN FP FN Precision Sensitivity Sensibility FYC 10 30 0 0 100% 100% 100% HY 9 29 1 1 95% 97% 90% LJG 9 29 1 1 95% 97% 90% LQF 10 30 0 0 100% 100% 100% 4 Multilinear Principal Component Analysis Multilinear principal component analysis, proposed in [16] is the multilinear extension of classical PCA method. The input and output data are considered to be tensor objects and contrary to PCA dimensionality reduction operates directly on tensors rather than its vectorized form. A tensor is a multidimensional object, whose elements are addressed by indices. The number of indices determines the order of the tensor, where each index defines one of the tensor modes [16]. In MPCA an elementary matrix algebra is extended by two operations: tensor unfolding and the product of a tensor and matrix. The unfolding transforms a tensor into a matrix according to a specified mode. The tensor is decomposed into column vectors, taken from the perspective of a specified mode, see Fig. 3. The tensor X multiplication by the matrix U according to mode n is obtained by the product of the unfolded tensor and the matrix U. To go back to a tensor space, an inverse unfolding operation is applied. In other words, the mode n of the tensor X is projected into the matrix U. Fig. 3. 1,2 and 3-mode tensor matrix product
Selection of Individual Gait Features Extracted by MPCA 263 The MPCA algorithm consists of the following steps: 1. Preprocessing - the normalization of input tenor samples to zero mean value. 2. Learning phase of MPCA - a loop with specified number of iterations, ∑ • Initialization - for each mode : o set matrix: Φ ∑ , where Φ denotes the desired matrix and is the input tensor sample in the -node vector subspace, determined by unfolding operation. o Eigen-decomposition of the matrix Φ , o Selection of most significant eigenvectors which form a projection matrix .Eigenvectors are evaluated by corresponding eigenvalues and the number of selected eigenvectors is determined by the variation cover ∑ , where specifies the dimensionality of mode and is i-th eigenvalue of matrix Φ . • Local optimization - for each mode update tensors: … 3. Reduction phase of MPCA - calculate the output tensors by their projection on the determined matrices . Our implementation of MPCA is based on Jama-1.0.2 library, supporting matrix operations and eigen decomposition. 5 Previous Work In [6] we proposed and examined method of gait identification based on the MPCA reduction and supervised learning. The experimental phase was carried out on the basis of dataset A of CASIA Gait Database. We considered two approaches of MPCA reduction called "Single dataset" and "train set and test set". In the first one all gait sequences are involved in learning phase of MPCA - determining the eigenvalues and eigenvectors. In the train set and test set approach, the gait database is divided into the training and test sets - two sequences of each actor are included in the training set and the remaining two in the test set. Similarly to the supervised classifiers, MPCA uses only the training set in the learning phase. In Fig. 4 the relationship between variation cover Q and obtained number of MPCA components is presented. For the maximum considered parameter Q = 0.99, each of gait sequences is reduced approximately twice from the initial size of 900 to about 500 thousands of attributes in both cases. A single attribute is obtained when Q is less than 0.08. The compression rate is very similar for both analyzed train datasets.
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Studies in Computational Intelligen
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Aleksander Nawrat · Zygmunt Kuś E
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“In God We Trust, All others we o
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VIII Preface valuable information i
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Contents Part I: Design of Object D
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Contents XIII Technology Developmen
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XVI List of Contributors Adam Czorn
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XVIII List of Contributors Henryk M
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XX List of Contributors Józef Wron
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2 Design of Object Detection, Recog
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4 A. Babiarz et al. 1 Introduction
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6 A. Babiarz et al. The description
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10 A. Babiarz et al. o o o “micvo
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12 A. Babiarz et al. a) b) Fig. 7.
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14 A. Babiarz et al. • The camera
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18 A. Babiarz et al. a) b) Fig. 11.
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Recognition and Location of Objects
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48 P. Demski et al. Fig. 1. Automat
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Omnidirectional Video Acquisition D
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Part III Design of Vision Based Con
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Vision System for Group of Mobile R
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184 D. Bereska et al. 4.1 Mechanica
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Probabilistic Approach to Planning
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206 Practical Applications of Class
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344 Conclusions Control algorithms
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[Studies in Computational Intelligence 481] Artur Babiarz, Robert Bieda, Karol Jędrasiak, Aleksander Nawrat (auth.), Aleksander Nawrat, Zygmunt Kuś (eds.) - Vision Based Systemsfor UAV Applications (2013, Sprin

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